LMFDB - Embedded newform 2.40.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,40,Mod(1,2)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 40, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$19.2679102779$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1050523661880 $ x^2 - x - 1050523661880
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.02495e6$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-524288. q^{2} +2.11161e9 q^{3} +2.74878e11 q^{4} +6.99557e13 q^{5} -1.10709e15 q^{6} +5.58800e16 q^{7} -1.44115e17 q^{8} +4.06359e17 q^{9} +O(q^{10})$	\(q-524288. q^{2} +2.11161e9 q^{3} +2.74878e11 q^{4} +6.99557e13 q^{5} -1.10709e15 q^{6} +5.58800e16 q^{7} -1.44115e17 q^{8} +4.06359e17 q^{9} -3.66769e19 q^{10} -2.13237e20 q^{11} +5.80436e20 q^{12} +1.59102e21 q^{13} -2.92972e22 q^{14} +1.47719e23 q^{15} +7.55579e22 q^{16} -2.01506e22 q^{17} -2.13049e23 q^{18} +7.01734e23 q^{19} +1.92293e25 q^{20} +1.17997e26 q^{21} +1.11797e26 q^{22} +1.72919e26 q^{23} -3.04316e26 q^{24} +3.07481e27 q^{25} -8.34153e26 q^{26} -7.69936e27 q^{27} +1.53602e28 q^{28} -3.91965e28 q^{29} -7.74476e28 q^{30} +1.95847e28 q^{31} -3.96141e28 q^{32} -4.50274e29 q^{33} +1.05647e28 q^{34} +3.90913e30 q^{35} +1.11699e29 q^{36} -2.47193e30 q^{37} -3.67911e29 q^{38} +3.35962e30 q^{39} -1.00817e31 q^{40} +3.59347e31 q^{41} -6.18644e31 q^{42} -4.72438e31 q^{43} -5.86141e31 q^{44} +2.84272e31 q^{45} -9.06593e31 q^{46} +2.11011e32 q^{47} +1.59549e32 q^{48} +2.21303e33 q^{49} -1.61209e33 q^{50} -4.25503e31 q^{51} +4.37337e32 q^{52} -2.04552e33 q^{53} +4.03668e33 q^{54} -1.49171e34 q^{55} -8.05316e33 q^{56} +1.48179e33 q^{57} +2.05502e34 q^{58} -8.82809e33 q^{59} +4.06048e34 q^{60} -1.48374e33 q^{61} -1.02680e34 q^{62} +2.27074e34 q^{63} +2.07692e34 q^{64} +1.11301e35 q^{65} +2.36073e35 q^{66} -5.72405e35 q^{67} -5.53895e33 q^{68} +3.65138e35 q^{69} -2.04951e36 q^{70} -7.39268e35 q^{71} -5.85626e34 q^{72} +3.13325e36 q^{73} +1.29600e36 q^{74} +6.49282e36 q^{75} +1.92891e35 q^{76} -1.19157e37 q^{77} -1.76141e36 q^{78} +1.73095e37 q^{79} +5.28570e36 q^{80} -1.79049e37 q^{81} -1.88401e37 q^{82} -2.82554e37 q^{83} +3.24348e37 q^{84} -1.40965e36 q^{85} +2.47694e37 q^{86} -8.27678e37 q^{87} +3.07307e37 q^{88} +1.03043e38 q^{89} -1.49040e37 q^{90} +8.89063e37 q^{91} +4.75316e37 q^{92} +4.13553e37 q^{93} -1.10631e38 q^{94} +4.90903e37 q^{95} -8.36497e37 q^{96} +3.18808e38 q^{97} -1.16027e39 q^{98} -8.66508e37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots - 31\!\cdots\!86 q^{9}+O(q^{10}) $ 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9	$ 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots + 72\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9 - 28113758147900866560 * q^10 - 432928873549526253816 * q^11 + 79004930825798025216 * q^12 - 1110716884377980399156 * q^13 - 3931107033531816083456 * q^14 + 177514053087296176226640 * q^15 + 151115727451828646838272 * q^16 - 361727800957394760654108 * q^17 + 166988256371990061907968 * q^18 + 11531090014904148017962360 * q^19 + 14739706031846649527009280 * q^20 + 206255336094912268749797184 * q^21 + 226979413255534020560683008 * q^22 + 733399930716618125168143824 * q^23 - 41421337172795995044446208 * q^24 + 1522590281438531446348943150 * q^25 + 582335533876762587512700928 * q^26 + 1015590507281331347888066160 * q^27 + 2061032244396328790762979328 * q^28 - 66283478621079021435470040660 * q^29 - 93068487865032337641512632320 * q^30 - 186790705491150225840859566656 * q^31 - 79228162514264337593543950336 * q^32 - 49512382311136707894463876512 * q^33 + 189649545308350584273820975104 * q^34 + 4699349644576524589906668345120 * q^35 - 87549938956757925577604726784 * q^36 + 2975477658591913559588340321052 * q^37 - 6045612121734065956041449799680 * q^38 + 8288123926734148196202973745808 * q^39 - 7727850996024816187216641392640 * q^40 + 16770326730060018362152407596724 * q^41 - 108137197650529363558293666004992 * q^42 - 9812395004866851368387130850616 * q^43 - 119002582616917420571719372898304 * q^44 + 40266363304618629851608344270540 * q^45 - 384512782875554283608155789197312 * q^46 + 672278426349701905666521369769632 * q^47 + 21716710023650866649862613499904 * q^48 + 3644309465778284633118680596157586 * q^49 - 798275813474844774943394706227200 * q^50 + 580553528426174218705101873396144 * q^51 - 305311532385180103481858944139264 * q^52 - 8761864571633558324701150169407236 * q^53 - 532461915881514649721538430894080 * q^54 - 11328905370645770966149273576022160 * q^55 - 1080574473350062429051540905918464 * q^56 - 18273076268563776391813920538819680 * q^57 + 34751632439288277990359716677550080 * q^58 - 12819225750671101391169533921560920 * q^59 + 48794691365782074237393374973788160 * q^60 - 20956924322550570450554426592045716 * q^61 + 97932125400544169605652580482940928 * q^62 + 57777775631084010576555882975543984 * q^63 + 41538374868278621028243970633760768 * q^64 + 155428501009224030268997780328195240 * q^65 + 25958747897141242308572676888723456 * q^66 - 430210910797386482647696776154188008 * q^67 - 99430980810624511127753051395325952 * q^68 - 657289380718196443693542397362196032 * q^69 - 2463812626455736924192987333326274560 * q^70 - 505835127408773713626404787885403536 * q^71 + 45901382395760699285231226996129792 * q^72 + 5225008613368893844954971696153387124 * q^73 - 1560007230667837176329451770243710976 * q^74 + 9324378759630332095186368293653381800 * q^75 + 3169641888079709971961059632574627840 * q^76 - 1286526284405007303669629309781343296 * q^77 - 4345363917299593089490864699242184704 * q^78 + 5133106059230199144047658337509305440 * q^79 + 4051619543003858829163438482464440320 * q^80 - 30865091955632000468542250095184041518 * q^81 - 8792481060649706907056161474071232512 * q^82 - 64869811713330760861780892502955295496 * q^83 + 56695035081800738961250669562425245696 * q^84 + 4169326167850982553612360321923472120 * q^85 + 5144520952311631770228952059407761408 * q^86 - 33355767685492704090236226944356001520 * q^87 + 62391626035058400596705606578106007552 * q^88 - 35854914207967073080588387127246110380 * q^89 - 21111171084251892207640035600912875520 * q^90 + 219621888597383210927045163285292559264 * q^91 + 201595437908258604244352782406680313856 * q^92 + 417824530946031783400120882011006743808 * q^93 - 352467511594032512718089155913780822016 * q^94 - 127785377061536603773906538331287257200 * q^95 - 11385810464879865574123169906637668352 * q^96 - 145570707650873901517300801294356641468 * q^97 - 1910667721193965293728526812398268448768 * q^98 + 72596170648714013699688849065341538088 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−524288.	−0.707107
$2$	−524288.	−0.707107
$3$	2.11161e9	1.04894	0.524469	−	0.851429i	$-0.324264\pi$
$3$	2.11161e9	1.04894	0.524469	+	0.851429i	$0.324264\pi$
$4$	2.74878e11	0.500000
$5$	6.99557e13	1.64024	0.820121	−	0.572190i	$-0.193906\pi$
$5$	6.99557e13	1.64024	0.820121	+	0.572190i	$0.193906\pi$
$6$	−1.10709e15	−0.741712
$7$	5.58800e16	1.85287	0.926435	−	0.376456i	$-0.122857\pi$
$7$	5.58800e16	1.85287	0.926435	+	0.376456i	$0.122857\pi$
$8$	−1.44115e17	−0.353553
$9$	4.06359e17	0.100272
$10$	−3.66769e19	−1.15983
$11$	−2.13237e20	−1.05125	−0.525623	−	0.850717i	$-0.676168\pi$
$11$	−2.13237e20	−1.05125	−0.525623	+	0.850717i	$0.676168\pi$
$12$	5.80436e20	0.524469
$13$	1.59102e21	0.301843	0.150921	−	0.988546i	$-0.451776\pi$
$13$	1.59102e21	0.301843	0.150921	+	0.988546i	$0.451776\pi$
$14$	−2.92972e22	−1.31018
$15$	1.47719e23	1.72051
$16$	7.55579e22	0.250000
$17$	−2.01506e22	−0.0204425	−0.0102212	−	0.999948i	$-0.503254\pi$
$17$	−2.01506e22	−0.0204425	−0.0102212	+	0.999948i	$0.503254\pi$
$18$	−2.13049e23	−0.0709033
$19$	7.01734e23	0.0813724	0.0406862	−	0.999172i	$-0.487046\pi$
$19$	7.01734e23	0.0813724	0.0406862	+	0.999172i	$0.487046\pi$
$20$	1.92293e25	0.820121
$21$	1.17997e26	1.94355
$22$	1.11797e26	0.743344
$23$	1.72919e26	0.483225	0.241613	−	0.970373i	$-0.422324\pi$
$23$	1.72919e26	0.483225	0.241613	+	0.970373i	$0.422324\pi$
$24$	−3.04316e26	−0.370856
$25$	3.07481e27	1.69040
$26$	−8.34153e26	−0.213435
$27$	−7.69936e27	−0.943759
$28$	1.53602e28	0.926435
$29$	−3.91965e28	−1.19258	−0.596288	−	0.802771i	$-0.703358\pi$
$29$	−3.91965e28	−1.19258	−0.596288	+	0.802771i	$0.703358\pi$
$30$	−7.74476e28	−1.21659
$31$	1.95847e28	0.162317	0.0811585	−	0.996701i	$-0.474138\pi$
$31$	1.95847e28	0.162317	0.0811585	+	0.996701i	$0.474138\pi$
$32$	−3.96141e28	−0.176777
$33$	−4.50274e29	−1.10269
$34$	1.05647e28	0.0144550
$35$	3.90913e30	3.03916
$36$	1.11699e29	0.0501362
$37$	−2.47193e30	−0.650282	−0.325141	−	0.945665i	$-0.605412\pi$
$37$	−2.47193e30	−0.650282	−0.325141	+	0.945665i	$0.605412\pi$
$38$	−3.67911e29	−0.0575390
$39$	3.35962e30	0.316614
$40$	−1.00817e31	−0.579913
$41$	3.59347e31	1.27711	0.638556	−	0.769576i	$-0.279532\pi$
$41$	3.59347e31	1.27711	0.638556	+	0.769576i	$0.279532\pi$
$42$	−6.18644e31	−1.37429
$43$	−4.72438e31	−0.663300	−0.331650	−	0.943402i	$-0.607605\pi$
$43$	−4.72438e31	−0.663300	−0.331650	+	0.943402i	$0.607605\pi$
$44$	−5.86141e31	−0.525623
$45$	2.84272e31	0.164471
$46$	−9.06593e31	−0.341692
$47$	2.11011e32	0.522874	0.261437	−	0.965220i	$-0.415804\pi$
$47$	2.11011e32	0.522874	0.261437	+	0.965220i	$0.415804\pi$
$48$	1.59549e32	0.262235
$49$	2.21303e33	2.43312
$50$	−1.61209e33	−1.19529
$51$	−4.25503e31	−0.0214429
$52$	4.37337e32	0.150921
$53$	−2.04552e33	−0.486883	−0.243441	−	0.969916i	$-0.578276\pi$
$53$	−2.04552e33	−0.486883	−0.243441	+	0.969916i	$0.578276\pi$
$54$	4.03668e33	0.667338
$55$	−1.49171e34	−1.72430
$56$	−8.05316e33	−0.655088
$57$	1.48179e33	0.0853547
$58$	2.05502e34	0.843278
$59$	−8.82809e33	−0.259569	−0.129784	−	0.991542i	$-0.541429\pi$
$59$	−8.82809e33	−0.259569	−0.129784	+	0.991542i	$0.541429\pi$
$60$	4.06048e34	0.860257
$61$	−1.48374e33	−0.0227733	−0.0113866	−	0.999935i	$-0.503625\pi$
$61$	−1.48374e33	−0.0227733	−0.0113866	+	0.999935i	$0.503625\pi$
$62$	−1.02680e34	−0.114775
$63$	2.27074e34	0.185792
$64$	2.07692e34	0.125000
$65$	1.11301e35	0.495095
$66$	2.36073e35	0.779722
$67$	−5.72405e35	−1.41008	−0.705041	−	0.709166i	$-0.749072\pi$
$67$	−5.72405e35	−1.41008	−0.705041	+	0.709166i	$0.749072\pi$
$68$	−5.53895e33	−0.0102212
$69$	3.65138e35	0.506874
$70$	−2.04951e36	−2.14901
$71$	−7.39268e35	−0.587847	−0.293924	−	0.955829i	$-0.594961\pi$
$71$	−7.39268e35	−0.587847	−0.293924	+	0.955829i	$0.594961\pi$
$72$	−5.85626e34	−0.0354516
$73$	3.13325e36	1.44944	0.724718	−	0.689046i	$-0.241970\pi$
$73$	3.13325e36	1.44944	0.724718	+	0.689046i	$0.241970\pi$
$74$	1.29600e36	0.459819
$75$	6.49282e36	1.77312
$76$	1.92891e35	0.0406862
$77$	−1.19157e37	−1.94782
$78$	−1.76141e36	−0.223880
$79$	1.73095e37	1.71616	0.858078	−	0.513519i	$-0.171658\pi$
$79$	1.73095e37	1.71616	0.858078	+	0.513519i	$0.171658\pi$
$80$	5.28570e36	0.410061
$81$	−1.79049e37	−1.09022
$82$	−1.88401e37	−0.903054
$83$	−2.82554e37	−1.06925	−0.534624	−	0.845090i	$-0.679547\pi$
$83$	−2.82554e37	−1.06925	−0.534624	+	0.845090i	$0.679547\pi$
$84$	3.24348e37	0.971773
$85$	−1.40965e36	−0.0335306
$86$	2.47694e37	0.469024
$87$	−8.27678e37	−1.25094
$88$	3.07307e37	0.371672
$89$	1.03043e38	0.999799	0.499900	−	0.866083i	$-0.333370\pi$
$89$	1.03043e38	0.999799	0.499900	+	0.866083i	$0.333370\pi$
$90$	−1.49040e37	−0.116299
$91$	8.89063e37	0.559275
$92$	4.75316e37	0.241613
$93$	4.13553e37	0.170261
$94$	−1.10631e38	−0.369728
$95$	4.90903e37	0.133471
$96$	−8.36497e37	−0.185428
$97$	3.18808e38	0.577404	0.288702	−	0.957419i	$-0.406776\pi$
$97$	3.18808e38	0.577404	0.288702	+	0.957419i	$0.406776\pi$
$98$	−1.16027e39	−1.72048
$99$	−8.66508e37	−0.105411
$100$	8.45198e38	0.845198
$101$	−2.20522e39	−1.81629	−0.908145	−	0.418655i	$-0.862501\pi$
$101$	−2.20522e39	−1.81629	−0.908145	+	0.418655i	$0.862501\pi$
$102$	2.23086e37	0.0151624
$103$	−2.38780e37	−0.0134175	−0.00670876	−	0.999977i	$-0.502135\pi$
$103$	−2.38780e37	−0.0134175	−0.00670876	+	0.999977i	$0.502135\pi$
$104$	−2.29290e38	−0.106718
$105$	8.25457e39	3.18789
$106$	1.07244e39	0.344278
$107$	2.85643e38	0.0763554	0.0381777	−	0.999271i	$-0.487845\pi$
$107$	2.85643e38	0.0763554	0.0381777	+	0.999271i	$0.487845\pi$
$108$	−2.11638e39	−0.471880
$109$	−9.31773e39	−1.73578	−0.867888	−	0.496760i	$-0.834523\pi$
$109$	−9.31773e39	−1.73578	−0.867888	+	0.496760i	$0.834523\pi$
$110$	7.82087e39	1.21926
$111$	−5.21976e39	−0.682106
$112$	4.22217e39	0.463217
$113$	−1.39501e40	−1.28691	−0.643453	−	0.765486i	$-0.722499\pi$
$113$	−1.39501e40	−1.28691	−0.643453	+	0.765486i	$0.722499\pi$
$114$	−7.76885e38	−0.0603549
$115$	1.20967e40	0.792607
$116$	−1.07742e40	−0.596288
$117$	6.46527e38	0.0302665
$118$	4.62846e39	0.183543
$119$	−1.12601e39	−0.0378772
$120$	−2.12886e40	−0.608294
$121$	4.32515e39	0.105120
$122$	7.77906e38	0.0161031
$123$	7.58802e40	1.33961
$124$	5.38340e39	0.0811585
$125$	8.78521e40	1.13242
$126$	−1.19052e40	−0.131375
$127$	−6.58469e40	−0.622820	−0.311410	−	0.950276i	$-0.600801\pi$
$127$	−6.58469e40	−0.622820	−0.311410	+	0.950276i	$0.600801\pi$
$128$	−1.08890e40	−0.0883883
$129$	−9.97607e40	−0.695761
$130$	−5.83538e40	−0.350085
$131$	−1.73109e40	−0.0894395	−0.0447197	−	0.999000i	$-0.514239\pi$
$131$	−1.73109e40	−0.0894395	−0.0447197	+	0.999000i	$0.514239\pi$
$132$	−1.23770e41	−0.551347
$133$	3.92129e40	0.150772
$134$	3.00105e41	0.997079
$135$	−5.38614e41	−1.54799
$136$	2.90400e39	0.00722751
$137$	−4.66027e40	−0.100545	−0.0502725	−	0.998736i	$-0.516009\pi$
$137$	−4.66027e40	−0.100545	−0.0502725	+	0.998736i	$0.516009\pi$
$138$	−1.91437e41	−0.358414
$139$	7.03916e41	1.14481	0.572403	−	0.819972i	$-0.306011\pi$
$139$	7.03916e41	1.14481	0.572403	+	0.819972i	$0.306011\pi$
$140$	1.07453e42	1.51958
$141$	4.45574e41	0.548463
$142$	3.87590e41	0.415671
$143$	−3.39264e41	−0.317311
$144$	3.07037e40	0.0250681
$145$	−2.74202e42	−1.95611
$146$	−1.64272e42	−1.02491
$147$	4.67307e42	2.55220
$148$	−6.79478e41	−0.325141
$149$	−2.62522e42	−1.10163	−0.550813	−	0.834629i	$-0.685682\pi$
$149$	−2.62522e42	−1.10163	−0.550813	+	0.834629i	$0.685682\pi$
$150$	−3.40411e42	−1.25379
$151$	3.83640e41	0.124129	0.0620645	−	0.998072i	$-0.480232\pi$
$151$	3.83640e41	0.124129	0.0620645	+	0.998072i	$0.480232\pi$
$152$	−1.01131e41	−0.0287695
$153$	−8.18838e39	−0.00204982
$154$	6.24725e42	1.37732
$155$	1.37006e42	0.266239
$156$	9.23486e41	0.158307
$157$	3.46715e42	0.524723	0.262361	−	0.964970i	$-0.415499\pi$
$157$	3.46715e42	0.524723	0.262361	+	0.964970i	$0.415499\pi$
$158$	−9.07518e42	−1.21351
$159$	−4.31935e42	−0.510710
$160$	−2.77123e42	−0.289957
$161$	9.66271e42	0.895353
$162$	9.38731e42	0.770900
$163$	1.55755e43	1.13444	0.567221	−	0.823565i	$-0.308018\pi$
$163$	1.55755e43	1.13444	0.567221	+	0.823565i	$0.308018\pi$
$164$	9.87766e42	0.638556
$165$	−3.14992e43	−1.80869
$166$	1.48140e43	0.756073
$167$	−1.67392e43	−0.759912	−0.379956	−	0.925005i	$-0.624061\pi$
$167$	−1.67392e43	−0.759912	−0.379956	+	0.925005i	$0.624061\pi$
$168$	−1.70052e43	−0.687147
$169$	−2.52524e43	−0.908891
$170$	7.39062e41	0.0237097
$171$	2.85156e41	0.00815941
$172$	−1.29863e43	−0.331650
$173$	−7.02710e43	−1.60279	−0.801396	−	0.598134i	$-0.795909\pi$
$173$	−7.02710e43	−1.60279	−0.801396	+	0.598134i	$0.795909\pi$
$174$	4.33942e43	0.884547
$175$	1.71821e44	3.13208
$176$	−1.61117e43	−0.262812
$177$	−1.86415e43	−0.272272
$178$	−5.40241e43	−0.706965
$179$	2.30853e43	0.270833	0.135416	−	0.990789i	$-0.456763\pi$
$179$	2.30853e43	0.270833	0.135416	+	0.990789i	$0.456763\pi$
$180$	7.81400e42	0.0822355
$181$	1.64061e44	1.54979	0.774897	−	0.632087i	$-0.217801\pi$
$181$	1.64061e44	1.54979	0.774897	+	0.632087i	$0.217801\pi$
$182$	−4.66125e43	−0.395467
$183$	−3.13308e42	−0.0238878
$184$	−2.49202e43	−0.170846
$185$	−1.72925e44	−1.06662
$186$	−2.16821e43	−0.120392
$187$	4.29685e42	0.0214901
$188$	5.80023e43	0.261437
$189$	−4.30240e44	−1.74866
$190$	−2.57375e43	−0.0943779
$191$	4.49011e44	1.48630	0.743150	−	0.669125i	$-0.233331\pi$
$191$	4.49011e44	1.48630	0.743150	+	0.669125i	$0.233331\pi$
$192$	4.38565e43	0.131117
$193$	−5.74657e44	−1.55253	−0.776267	−	0.630404i	$-0.782889\pi$
$193$	−5.74657e44	−1.55253	−0.776267	+	0.630404i	$0.782889\pi$
$194$	−1.67147e44	−0.408286
$195$	2.35025e44	0.519325
$196$	6.08314e44	1.21656
$197$	5.13860e44	0.930579	0.465290	−	0.885159i	$-0.345950\pi$
$197$	5.13860e44	0.930579	0.465290	+	0.885159i	$0.345950\pi$
$198$	4.54300e43	0.0745369
$199$	7.59958e44	1.13020	0.565099	−	0.825023i	$-0.308838\pi$
$199$	7.59958e44	1.13020	0.565099	+	0.825023i	$0.308838\pi$
$200$	−4.43127e44	−0.597645
$201$	−1.20870e45	−1.47909
$202$	1.15617e45	1.28431
$203$	−2.19030e45	−2.20969
$204$	−1.16961e43	−0.0107215
$205$	2.51384e45	2.09477
$206$	1.25190e43	0.00948763
$207$	7.02672e43	0.0484542
$208$	1.20214e44	0.0754607
$209$	−1.49635e44	−0.0855425
$210$	−4.32777e45	−2.25418
$211$	2.02926e45	0.963450	0.481725	−	0.876323i	$-0.340010\pi$
$211$	2.02926e45	0.963450	0.481725	+	0.876323i	$0.340010\pi$
$212$	−5.62268e44	−0.243441
$213$	−1.56105e45	−0.616616
$214$	−1.49759e44	−0.0539914
$215$	−3.30498e45	−1.08797
$216$	1.10959e45	0.333669
$217$	1.09439e45	0.300752
$218$	4.88518e45	1.22738
$219$	6.61621e45	1.52037
$220$	−4.10039e45	−0.862150
$221$	−3.20600e43	−0.00617041
$222$	2.73665e45	0.482322
$223$	5.13225e45	0.828634	0.414317	−	0.910133i	$-0.364021\pi$
$223$	5.13225e45	0.828634	0.414317	+	0.910133i	$0.364021\pi$
$224$	−2.21364e45	−0.327544
$225$	1.24948e45	0.169500
$226$	7.31386e45	0.909980
$227$	−1.27586e46	−1.45647	−0.728233	−	0.685330i	$-0.759658\pi$
$227$	−1.27586e46	−1.45647	−0.728233	+	0.685330i	$0.759658\pi$
$228$	4.07312e44	0.0426773
$229$	−6.28548e45	−0.604709	−0.302354	−	0.953196i	$-0.597773\pi$
$229$	−6.28548e45	−0.604709	−0.302354	+	0.953196i	$0.597773\pi$
$230$	−6.34214e45	−0.560458
$231$	−2.51613e46	−2.04315
$232$	5.64881e45	0.421639
$233$	4.89903e45	0.336256	0.168128	−	0.985765i	$-0.446228\pi$
$233$	4.89903e45	0.336256	0.168128	+	0.985765i	$0.446228\pi$
$234$	−3.38966e44	−0.0214016
$235$	1.47614e46	0.857641
$236$	−2.42665e45	−0.129784
$237$	3.65510e46	1.80014
$238$	5.90356e44	0.0267833
$239$	−3.74803e46	−1.56691	−0.783456	−	0.621447i	$-0.786545\pi$
$239$	−3.74803e46	−1.56691	−0.783456	+	0.621447i	$0.786545\pi$
$240$	1.11614e46	0.430129
$241$	−2.06478e46	−0.733738	−0.366869	−	0.930273i	$-0.619570\pi$
$241$	−2.06478e46	−0.733738	−0.366869	+	0.930273i	$0.619570\pi$
$242$	−2.26762e45	−0.0743312
$243$	−6.60610e45	−0.199813
$244$	−4.07847e44	−0.0113866
$245$	1.54814e47	3.99091
$246$	−3.97831e46	−0.947249
$247$	1.11647e45	0.0245617
$248$	−2.82245e45	−0.0573877
$249$	−5.96645e46	−1.12158
$250$	−4.60598e46	−0.800740
$251$	−1.14305e46	−0.183834	−0.0919171	−	0.995767i	$-0.529299\pi$
$251$	−1.14305e46	−0.183834	−0.0919171	+	0.995767i	$0.529299\pi$
$252$	6.24176e45	0.0928958
$253$	−3.68727e46	−0.507989
$254$	3.45227e46	0.440401
$255$	−2.97663e45	−0.0351716
$256$	5.70899e45	0.0625000
$257$	−4.39223e46	−0.445645	−0.222823	−	0.974859i	$-0.571527\pi$
$257$	−4.39223e46	−0.445645	−0.222823	+	0.974859i	$0.571527\pi$
$258$	5.23033e46	0.491977
$259$	−1.38131e47	−1.20489
$260$	3.05942e46	0.247548
$261$	−1.59279e46	−0.119582
$262$	9.07589e45	0.0632432
$263$	1.65701e47	1.07198	0.535991	−	0.844224i	$-0.319938\pi$
$263$	1.65701e47	1.07198	0.535991	+	0.844224i	$0.319938\pi$
$264$	6.48913e46	0.389861
$265$	−1.43096e47	−0.798606
$266$	−2.05589e46	−0.106612
$267$	2.17587e47	1.04873
$268$	−1.57341e47	−0.705041
$269$	1.06675e47	0.444523	0.222261	−	0.974987i	$-0.428656\pi$
$269$	1.06675e47	0.444523	0.222261	+	0.974987i	$0.428656\pi$
$270$	2.82389e47	1.09460
$271$	8.51889e46	0.307243	0.153621	−	0.988130i	$-0.450906\pi$
$271$	8.51889e46	0.307243	0.153621	+	0.988130i	$0.450906\pi$
$272$	−1.52253e45	−0.00511062
$273$	1.87736e47	0.586645
$274$	2.44333e46	0.0710960
$275$	−6.55663e47	−1.77702
$276$	1.00368e47	0.253437
$277$	−2.87740e47	−0.677087	−0.338544	−	0.940951i	$-0.609934\pi$
$277$	−2.87740e47	−0.677087	−0.338544	+	0.940951i	$0.609934\pi$
$278$	−3.69055e47	−0.809500
$279$	7.95843e45	0.0162759
$280$	−5.63365e47	−1.07450
$281$	9.08114e46	0.161572	0.0807862	−	0.996731i	$-0.474257\pi$
$281$	9.08114e46	0.161572	0.0807862	+	0.996731i	$0.474257\pi$
$282$	−2.33609e47	−0.387822
$283$	3.51812e47	0.545099	0.272550	−	0.962142i	$-0.412133\pi$
$283$	3.51812e47	0.545099	0.272550	+	0.962142i	$0.412133\pi$
$284$	−2.03209e47	−0.293924
$285$	1.03660e47	0.140002
$286$	1.77872e47	0.224373
$287$	2.00803e48	2.36632
$288$	−1.60976e46	−0.0177258
$289$	−9.71240e47	−0.999582
$290$	1.43761e48	1.38318
$291$	6.73199e47	0.605661
$292$	8.61260e47	0.724718
$293$	−1.82981e48	−1.44041	−0.720206	−	0.693760i	$-0.755953\pi$
$293$	−1.82981e48	−1.44041	−0.720206	+	0.693760i	$0.755953\pi$
$294$	−2.45004e48	−1.80468
$295$	−6.17576e47	−0.425756
$296$	3.56242e47	0.229910
$297$	1.64179e48	0.992124
$298$	1.37637e48	0.778967
$299$	2.75118e47	0.145858
$300$	1.78473e48	0.886561
$301$	−2.63999e48	−1.22901
$302$	−2.01138e47	−0.0877725
$303$	−4.65658e48	−1.90518
$304$	5.30215e46	0.0203431
$305$	−1.03796e47	−0.0373537
$306$	4.29307e45	0.00144944
$307$	4.87373e48	1.54406	0.772028	−	0.635588i	$-0.219242\pi$
$307$	4.87373e48	1.54406	0.772028	+	0.635588i	$0.219242\pi$
$308$	−3.27536e48	−0.973912
$309$	−5.04212e46	−0.0140742
$310$	−7.18307e47	−0.188260
$311$	1.73314e48	0.426585	0.213293	−	0.976988i	$-0.431581\pi$
$311$	1.73314e48	0.426585	0.213293	+	0.976988i	$0.431581\pi$
$312$	−4.84173e47	−0.111940
$313$	−1.94529e48	−0.422541	−0.211271	−	0.977428i	$-0.567760\pi$
$313$	−1.94529e48	−0.422541	−0.211271	+	0.977428i	$0.567760\pi$
$314$	−1.81779e48	−0.371035
$315$	1.58851e48	0.304743
$316$	4.75801e48	0.858078
$317$	2.01018e48	0.340863	0.170432	−	0.985370i	$-0.445484\pi$
$317$	2.01018e48	0.340863	0.170432	+	0.985370i	$0.445484\pi$
$318$	2.26458e48	0.361126
$319$	8.35813e48	1.25369
$320$	1.45292e48	0.205030
$321$	6.03168e47	0.0800922
$322$	−5.06604e48	−0.633110
$323$	−1.41403e46	−0.00166345
$324$	−4.92165e48	−0.545109
$325$	4.89209e48	0.510234
$326$	−8.16603e48	−0.802172
$327$	−1.96755e49	−1.82072
$328$	−5.17874e48	−0.451527
$329$	1.17913e49	0.968818
$330$	1.65147e49	1.27893
$331$	−8.96177e48	−0.654256	−0.327128	−	0.944980i	$-0.606081\pi$
$331$	−8.96177e48	−0.654256	−0.327128	+	0.944980i	$0.606081\pi$
$332$	−7.76678e48	−0.534624
$333$	−1.00449e48	−0.0652054
$334$	8.77616e48	0.537339
$335$	−4.00430e49	−2.31288
$336$	8.91560e48	0.485887
$337$	2.66398e49	1.37009	0.685044	−	0.728502i	$-0.259783\pi$
$337$	2.66398e49	1.37009	0.685044	+	0.728502i	$0.259783\pi$
$338$	1.32395e49	0.642683
$339$	−2.94572e49	−1.34989
$340$	−3.87481e47	−0.0167653
$341$	−4.17618e48	−0.170635
$342$	−1.49504e47	−0.00576957
$343$	7.28390e49	2.65539
$344$	6.80855e48	0.234512
$345$	2.55435e49	0.831396
$346$	3.68423e49	1.13335
$347$	1.24516e49	0.362077	0.181038	−	0.983476i	$-0.442054\pi$
$347$	1.24516e49	0.362077	0.181038	+	0.983476i	$0.442054\pi$
$348$	−2.27510e49	−0.625469
$349$	−6.48032e49	−1.68461	−0.842307	−	0.538998i	$-0.818803\pi$
$349$	−6.48032e49	−1.68461	−0.842307	+	0.538998i	$0.818803\pi$
$350$	−9.00835e49	−2.21472
$351$	−1.22498e49	−0.284867
$352$	8.44718e48	0.185836
$353$	2.51734e49	0.524005	0.262002	−	0.965067i	$-0.415617\pi$
$353$	2.51734e49	0.524005	0.262002	+	0.965067i	$0.415617\pi$
$354$	9.77353e48	0.192525
$355$	−5.17161e49	−0.964212
$356$	2.83242e49	0.499900
$357$	−2.37771e48	−0.0397309
$358$	−1.21033e49	−0.191508
$359$	8.44531e49	1.26553	0.632767	−	0.774342i	$-0.281919\pi$
$359$	8.44531e49	1.26553	0.632767	+	0.774342i	$0.281919\pi$
$360$	−4.09679e48	−0.0581493
$361$	−7.38763e49	−0.993379
$362$	−8.60154e49	−1.09587
$363$	9.13304e48	0.110265
$364$	2.44384e49	0.279638
$365$	2.19189e50	2.37743
$366$	1.64264e48	0.0168912
$367$	−1.47599e50	−1.43912	−0.719559	−	0.694432i	$-0.755656\pi$
$367$	−1.47599e50	−1.43912	−0.719559	+	0.694432i	$0.755656\pi$
$368$	1.30654e49	0.120806
$369$	1.46024e49	0.128059
$370$	9.06627e49	0.754215
$371$	−1.14304e50	−0.902130
$372$	1.13677e49	0.0851303
$373$	8.85925e48	0.0629615	0.0314807	−	0.999504i	$-0.489978\pi$
$373$	8.85925e48	0.0629615	0.0314807	+	0.999504i	$0.489978\pi$
$374$	−2.25278e48	−0.0151958
$375$	1.85510e50	1.18784
$376$	−3.04099e49	−0.184864
$377$	−6.23624e49	−0.359970
$378$	2.25570e50	1.23649
$379$	1.64631e50	0.857130	0.428565	−	0.903511i	$-0.359019\pi$
$379$	1.64631e50	0.857130	0.428565	+	0.903511i	$0.359019\pi$
$380$	1.34938e49	0.0667353
$381$	−1.39043e50	−0.653300
$382$	−2.35411e50	−1.05097
$383$	−1.41005e50	−0.598216	−0.299108	−	0.954219i	$-0.596689\pi$
$383$	−1.41005e50	−0.598216	−0.299108	+	0.954219i	$0.596689\pi$
$384$	−2.29934e49	−0.0927140
$385$	−8.33570e50	−3.19490
$386$	3.01286e50	1.09781
$387$	−1.91980e49	−0.0665107
$388$	8.76332e49	0.288702
$389$	3.89871e50	1.22153	0.610764	−	0.791813i	$-0.290863\pi$
$389$	3.89871e50	1.22153	0.610764	+	0.791813i	$0.290863\pi$
$390$	−1.23221e50	−0.367218
$391$	−3.48442e48	−0.00987832
$392$	−3.18932e50	−0.860239
$393$	−3.65539e49	−0.0938165
$394$	−2.69411e50	−0.658019
$395$	1.21090e51	2.81491
$396$	−2.38184e49	−0.0527055
$397$	3.86542e50	0.814295	0.407148	−	0.913362i	$-0.366523\pi$
$397$	3.86542e50	0.814295	0.407148	+	0.913362i	$0.366523\pi$
$398$	−3.98437e50	−0.799171
$399$	8.28025e49	0.158151
$400$	2.32326e50	0.422599
$401$	−1.82356e49	−0.0315940	−0.0157970	−	0.999875i	$-0.505029\pi$
$401$	−1.82356e49	−0.0315940	−0.0157970	+	0.999875i	$0.505029\pi$
$402$	6.33706e50	1.04588
$403$	3.11597e49	0.0489942
$404$	−6.06166e50	−0.908145
$405$	−1.25255e51	−1.78822
$406$	1.14835e51	1.56248
$407$	5.27106e50	0.683607
$408$	6.13214e48	0.00758121
$409$	−6.35184e48	−0.00748678	−0.00374339	−	0.999993i	$-0.501192\pi$
$409$	−6.35184e48	−0.00748678	−0.00374339	+	0.999993i	$0.501192\pi$
$410$	−1.31798e51	−1.48123
$411$	−9.84070e49	−0.105466
$412$	−6.56354e48	−0.00670876
$413$	−4.93314e50	−0.480947
$414$	−3.68403e49	−0.0342623
$415$	−1.97663e51	−1.75383
$416$	−6.30269e49	−0.0533588
$417$	1.48640e51	1.20083
$418$	7.84521e49	0.0604877
$419$	−1.06807e51	−0.786004	−0.393002	−	0.919538i	$-0.628563\pi$
$419$	−1.06807e51	−0.786004	−0.393002	+	0.919538i	$0.628563\pi$
$420$	2.26900e51	1.59394
$421$	6.88098e50	0.461476	0.230738	−	0.973016i	$-0.425886\pi$
$421$	6.88098e50	0.461476	0.230738	+	0.973016i	$0.425886\pi$
$422$	−1.06391e51	−0.681262
$423$	8.57464e49	0.0524299
$424$	2.94790e50	0.172139
$425$	−6.19593e49	−0.0345559
$426$	8.18440e50	0.436013
$427$	−8.29113e49	−0.0421959
$428$	7.85169e49	0.0381777
$429$	−7.16395e50	−0.332840
$430$	1.73276e51	0.769313
$431$	3.46368e51	1.46971	0.734855	−	0.678225i	$-0.237250\pi$
$431$	3.46368e51	1.46971	0.734855	+	0.678225i	$0.237250\pi$
$432$	−5.81747e50	−0.235940
$433$	2.79988e51	1.08549	0.542745	−	0.839898i	$-0.317385\pi$
$433$	2.79988e51	1.08549	0.542745	+	0.839898i	$0.317385\pi$
$434$	−5.73777e50	−0.212664
$435$	−5.79008e51	−2.05184
$436$	−2.56124e51	−0.867888
$437$	1.21343e50	0.0393212
$438$	−3.46880e51	−1.07506
$439$	5.61218e50	0.166369	0.0831847	−	0.996534i	$-0.473491\pi$
$439$	5.61218e50	0.166369	0.0831847	+	0.996534i	$0.473491\pi$
$440$	2.14979e51	0.609632
$441$	8.99287e50	0.243975
$442$	1.68087e49	0.00436314
$443$	3.83235e51	0.951902	0.475951	−	0.879472i	$-0.342104\pi$
$443$	3.83235e51	0.951902	0.475951	+	0.879472i	$0.342104\pi$
$444$	−1.43480e51	−0.341053
$445$	7.20844e51	1.63991
$446$	−2.69078e51	−0.585933
$447$	−5.54346e51	−1.15554
$448$	1.16058e51	0.231609
$449$	−8.58209e51	−1.63979	−0.819897	−	0.572511i	$-0.805970\pi$
$449$	−8.58209e51	−1.63979	−0.819897	+	0.572511i	$0.805970\pi$
$450$	−6.55087e50	−0.119855
$451$	−7.66260e51	−1.34256
$452$	−3.83457e51	−0.643453
$453$	8.10100e50	0.130204
$454$	6.68920e51	1.02988
$455$	6.21950e51	0.917347
$456$	−2.13549e50	−0.0301774
$457$	1.22325e52	1.65634	0.828172	−	0.560474i	$-0.189381\pi$
$457$	1.22325e52	1.65634	0.828172	+	0.560474i	$0.189381\pi$
$458$	3.29540e51	0.427594
$459$	1.55147e50	0.0192928
$460$	3.32511e51	0.396303
$461$	−2.33460e51	−0.266713	−0.133357	−	0.991068i	$-0.542576\pi$
$461$	−2.33460e51	−0.266713	−0.133357	+	0.991068i	$0.542576\pi$
$462$	1.31918e52	1.44472
$463$	−1.88861e51	−0.198296	−0.0991479	−	0.995073i	$-0.531612\pi$
$463$	−1.88861e51	−0.198296	−0.0991479	+	0.995073i	$0.531612\pi$
$464$	−2.96160e51	−0.298144
$465$	2.89304e51	0.279269
$466$	−2.56850e51	−0.237769
$467$	6.32486e50	0.0561528	0.0280764	−	0.999606i	$-0.491062\pi$
$467$	6.32486e50	0.0561528	0.0280764	+	0.999606i	$0.491062\pi$
$468$	1.77716e50	0.0151332
$469$	−3.19860e52	−2.61270
$470$	−7.73925e51	−0.606444
$471$	7.32129e51	0.550402
$472$	1.27226e51	0.0917715
$473$	1.00741e52	0.697292
$474$	−1.91633e52	−1.27289
$475$	2.15770e51	0.137552
$476$	−3.09517e50	−0.0189386
$477$	−8.31216e50	−0.0488209
$478$	1.96505e52	1.10797
$479$	−3.35581e52	−1.81658	−0.908290	−	0.418342i	$-0.862611\pi$
$479$	−3.35581e52	−1.81658	−0.908290	+	0.418342i	$0.862611\pi$
$480$	−5.85177e51	−0.304147
$481$	−3.93289e51	−0.196283
$482$	1.08254e52	0.518831
$483$	2.04039e52	0.939170
$484$	1.18889e51	0.0525601
$485$	2.23024e52	0.947083
$486$	3.46350e51	0.141289
$487$	1.21303e52	0.475397	0.237698	−	0.971339i	$-0.423607\pi$
$487$	1.21303e52	0.475397	0.237698	+	0.971339i	$0.423607\pi$
$488$	2.13829e50	0.00805157
$489$	3.28894e52	1.18996
$490$	−8.11673e52	−2.82200
$491$	2.92375e52	0.976902	0.488451	−	0.872591i	$-0.337562\pi$
$491$	2.92375e52	0.976902	0.488451	+	0.872591i	$0.337562\pi$
$492$	2.08578e52	0.669806
$493$	7.89831e50	0.0243792
$494$	−5.85354e50	−0.0173677
$495$	−6.06172e51	−0.172900
$496$	1.47978e51	0.0405793
$497$	−4.13103e52	−1.08920
$498$	3.12814e52	0.793074
$499$	3.77527e52	0.920422	0.460211	−	0.887810i	$-0.347774\pi$
$499$	3.77527e52	0.920422	0.460211	+	0.887810i	$0.347774\pi$
$500$	2.41486e52	0.566209
$501$	−3.53467e52	−0.797101
$502$	5.99286e51	0.129990
$503$	2.28414e52	0.476592	0.238296	−	0.971193i	$-0.423411\pi$
$503$	2.28414e52	0.476592	0.238296	+	0.971193i	$0.423411\pi$
$504$	−3.27248e51	−0.0656873
$505$	−1.54268e53	−2.97916
$506$	1.93319e52	0.359202
$507$	−5.33233e52	−0.953371
$508$	−1.80999e52	−0.311410
$509$	−2.74724e52	−0.454883	−0.227442	−	0.973792i	$-0.573036\pi$
$509$	−2.74724e52	−0.454883	−0.227442	+	0.973792i	$0.573036\pi$
$510$	1.56061e51	0.0248701
$511$	1.75086e53	2.68561
$512$	−2.99316e51	−0.0441942
$513$	−5.40290e51	−0.0767960
$514$	2.30279e52	0.315119
$515$	−1.67040e51	−0.0220080
$516$	−2.74220e52	−0.347881
$517$	−4.49954e52	−0.549670
$518$	7.24206e52	0.851984
$519$	−1.48385e53	−1.68123
$520$	−1.60402e52	−0.175043
$521$	1.42787e53	1.50091	0.750453	−	0.660924i	$-0.229835\pi$
$521$	1.42787e53	1.50091	0.750453	+	0.660924i	$0.229835\pi$
$522$	8.35078e51	0.0845575
$523$	−7.92499e52	−0.773064	−0.386532	−	0.922276i	$-0.626327\pi$
$523$	−7.92499e52	−0.773064	−0.386532	+	0.922276i	$0.626327\pi$
$524$	−4.75838e51	−0.0447197
$525$	3.62819e53	3.28536
$526$	−8.68749e52	−0.758005
$527$	−3.94643e50	−0.00331816
$528$	−3.40217e52	−0.275673
$529$	−9.81508e52	−0.766493
$530$	7.50234e52	0.564699
$531$	−3.58738e51	−0.0260276
$532$	1.07788e52	0.0753862
$533$	5.71729e52	0.385487
$534$	−1.14078e53	−0.741563
$535$	1.99824e52	0.125241
$536$	8.24922e52	0.498540
$537$	4.87472e52	0.284087
$538$	−5.59285e52	−0.314325
$539$	−4.71900e53	−2.55781
$540$	−1.48053e53	−0.773997
$541$	1.07392e53	0.541534	0.270767	−	0.962645i	$-0.412723\pi$
$541$	1.07392e53	0.541534	0.270767	+	0.962645i	$0.412723\pi$
$542$	−4.46635e52	−0.217253
$543$	3.46434e53	1.62564
$544$	7.98247e50	0.00361375
$545$	−6.51829e53	−2.84709
$546$	−9.84276e52	−0.414821
$547$	2.11050e53	0.858288	0.429144	−	0.903236i	$-0.358815\pi$
$547$	2.11050e53	0.858288	0.429144	+	0.903236i	$0.358815\pi$
$548$	−1.28101e52	−0.0502725
$549$	−6.02931e50	−0.00228353
$550$	3.43756e53	1.25655
$551$	−2.75055e52	−0.0970428
$552$	−5.26219e52	−0.179207
$553$	9.67256e53	3.17981
$554$	1.50859e53	0.478773
$555$	−3.65152e53	−1.11882
$556$	1.93491e53	0.572403
$557$	−9.48009e52	−0.270792	−0.135396	−	0.990792i	$-0.543231\pi$
$557$	−9.48009e52	−0.270792	−0.135396	+	0.990792i	$0.543231\pi$
$558$	−4.17251e51	−0.0115088
$559$	−7.51659e52	−0.200212
$560$	2.95365e53	0.759789
$561$	9.07328e51	0.0225418
$562$	−4.76113e52	−0.114249
$563$	1.70902e53	0.396127	0.198064	−	0.980189i	$-0.436535\pi$
$563$	1.70902e53	0.396127	0.198064	+	0.980189i	$0.436535\pi$
$564$	1.22479e53	0.274232
$565$	−9.75888e53	−2.11084
$566$	−1.84451e53	−0.385443
$567$	−1.00052e54	−2.02003
$568$	1.06540e53	0.207835
$569$	2.43029e53	0.458109	0.229055	−	0.973414i	$-0.426437\pi$
$569$	2.43029e53	0.458109	0.229055	+	0.973414i	$0.426437\pi$
$570$	−5.43476e52	−0.0989967
$571$	4.94837e53	0.871079	0.435540	−	0.900170i	$-0.356558\pi$
$571$	4.94837e53	0.871079	0.435540	+	0.900170i	$0.356558\pi$
$572$	−9.32563e52	−0.158656
$573$	9.48138e53	1.55904
$574$	−1.05279e54	−1.67324
$575$	5.31693e53	0.816842
$576$	8.43976e51	0.0125341
$577$	1.04767e54	1.50417	0.752087	−	0.659064i	$-0.229047\pi$
$577$	1.04767e54	1.50417	0.752087	+	0.659064i	$0.229047\pi$
$578$	5.09209e53	0.706811
$579$	−1.21345e54	−1.62851
$580$	−7.53720e53	−0.978057
$581$	−1.57891e54	−1.98118
$582$	−3.52950e53	−0.428267
$583$	4.36180e53	0.511834
$584$	−4.51548e53	−0.512453
$585$	4.52282e52	0.0496444
$586$	9.59346e53	1.01853
$587$	1.22834e54	1.26146	0.630732	−	0.776001i	$-0.282755\pi$
$587$	1.22834e54	1.26146	0.630732	+	0.776001i	$0.282755\pi$
$588$	1.28452e54	1.27610
$589$	1.37433e52	0.0132081
$590$	3.23787e53	0.301055
$591$	1.08507e54	0.976120
$592$	−1.86773e53	−0.162571
$593$	−6.09903e53	−0.513682	−0.256841	−	0.966454i	$-0.582682\pi$
$593$	−6.09903e53	−0.513682	−0.256841	+	0.966454i	$0.582682\pi$
$594$	−8.60769e53	−0.701538
$595$	−7.87712e52	−0.0621279
$596$	−7.21616e53	−0.550813
$597$	1.60474e54	1.18551
$598$	−1.44241e53	−0.103137
$599$	1.96361e52	0.0135904	0.00679520	−	0.999977i	$-0.497837\pi$
$599$	1.96361e52	0.0135904	0.00679520	+	0.999977i	$0.497837\pi$
$600$	−9.35714e53	−0.626893
$601$	−1.10020e54	−0.713545	−0.356772	−	0.934191i	$-0.616123\pi$
$601$	−1.10020e54	−0.713545	−0.356772	+	0.934191i	$0.616123\pi$
$602$	1.38411e54	0.869040
$603$	−2.32602e53	−0.141392
$604$	1.05454e53	0.0620645
$605$	3.02569e53	0.172423
$606$	2.44139e54	1.34716
$607$	−2.17795e54	−1.16377	−0.581886	−	0.813270i	$-0.697685\pi$
$607$	−2.17795e54	−1.16377	−0.581886	+	0.813270i	$0.697685\pi$
$608$	−2.77985e52	−0.0143847
$609$	−4.62507e54	−2.31783
$610$	5.44190e52	0.0264131
$611$	3.35723e53	0.157826
$612$	−2.25080e51	−0.00102491
$613$	−3.60972e54	−1.59219	−0.796094	−	0.605172i	$-0.793104\pi$
$613$	−3.60972e54	−1.59219	−0.796094	+	0.605172i	$0.793104\pi$
$614$	−2.55524e54	−1.09181
$615$	5.30826e54	2.19729
$616$	1.71723e54	0.688659
$617$	3.42895e54	1.33230	0.666148	−	0.745820i	$-0.267942\pi$
$617$	3.42895e54	1.33230	0.666148	+	0.745820i	$0.267942\pi$
$618$	2.64352e52	0.00995194
$619$	−4.35180e54	−1.58746	−0.793728	−	0.608273i	$-0.791863\pi$
$619$	−4.35180e54	−1.58746	−0.793728	+	0.608273i	$0.791863\pi$
$620$	3.76600e53	0.133120
$621$	−1.33136e54	−0.456048
$622$	−9.08664e53	−0.301641
$623$	5.75804e54	1.85250
$624$	2.53846e53	0.0791536
$625$	5.52702e53	0.167044
$626$	1.01989e54	0.298782
$627$	−3.15972e53	−0.0897289
$628$	9.53044e53	0.262361
$629$	4.98108e52	0.0132934
$630$	−8.32837e53	−0.215486
$631$	7.04397e54	1.76703	0.883517	−	0.468399i	$-0.155169\pi$
$631$	7.04397e54	1.76703	0.883517	+	0.468399i	$0.155169\pi$
$632$	−2.49457e54	−0.606753
$633$	4.28501e54	1.01060
$634$	−1.05392e54	−0.241027
$635$	−4.60637e54	−1.02158
$636$	−1.18729e54	−0.255355
$637$	3.52098e54	0.734421
$638$	−4.38207e54	−0.886494
$639$	−3.00409e53	−0.0589448
$640$	−7.61750e53	−0.144978
$641$	−3.16978e54	−0.585191	−0.292596	−	0.956236i	$-0.594519\pi$
$641$	−3.16978e54	−0.585191	−0.292596	+	0.956236i	$0.594519\pi$
$642$	−3.16234e53	−0.0566337
$643$	−1.02473e55	−1.78032	−0.890158	−	0.455653i	$-0.849406\pi$
$643$	−1.02473e55	−1.78032	−0.890158	+	0.455653i	$0.849406\pi$
$644$	2.65607e54	0.447677
$645$	−6.97883e54	−1.14122
$646$	7.41361e51	0.00117624
$647$	−2.95656e54	−0.455149	−0.227574	−	0.973761i	$-0.573080\pi$
$647$	−2.95656e54	−0.455149	−0.227574	+	0.973761i	$0.573080\pi$
$648$	2.58036e54	0.385450
$649$	1.88247e54	0.272871
$650$	−2.56487e54	−0.360790
$651$	2.31094e54	0.315471
$652$	4.28135e54	0.567221
$653$	1.14432e55	1.47143	0.735713	−	0.677293i	$-0.236847\pi$
$653$	1.14432e55	1.47143	0.735713	+	0.677293i	$0.236847\pi$
$654$	1.03156e55	1.28744
$655$	−1.21100e54	−0.146702
$656$	2.71515e54	0.319278
$657$	1.27322e54	0.145338
$658$	−6.18204e54	−0.685058
$659$	−7.41507e54	−0.797719	−0.398859	−	0.917012i	$-0.630594\pi$
$659$	−7.41507e54	−0.797719	−0.398859	+	0.917012i	$0.630594\pi$
$660$	−8.65844e54	−0.904343
$661$	3.87545e54	0.393001	0.196501	−	0.980504i	$-0.437042\pi$
$661$	3.87545e54	0.393001	0.196501	+	0.980504i	$0.437042\pi$
$662$	4.69855e54	0.462629
$663$	−6.76984e52	−0.00647239
$664$	4.07203e54	0.378036
$665$	2.74317e54	0.247303
$666$	5.26642e53	0.0461072
$667$	−6.77781e54	−0.576283
$668$	−4.60123e54	−0.379956
$669$	1.08373e55	0.869186
$670$	2.09941e55	1.63545
$671$	3.16388e53	0.0239403
$672$	−4.67434e54	−0.343574
$673$	−7.42773e54	−0.530350	−0.265175	−	0.964200i	$-0.585430\pi$
$673$	−7.42773e54	−0.530350	−0.265175	+	0.964200i	$0.585430\pi$
$674$	−1.39669e55	−0.968799
$675$	−2.36741e55	−1.59533
$676$	−6.94132e54	−0.454445
$677$	1.99160e55	1.26684	0.633421	−	0.773807i	$-0.281650\pi$
$677$	1.99160e55	1.26684	0.633421	+	0.773807i	$0.281650\pi$
$678$	1.54440e55	0.954513
$679$	1.78150e55	1.06985
$680$	2.03152e53	0.0118549
$681$	−2.69413e55	−1.52774
$682$	2.18952e54	0.120657
$683$	9.66545e54	0.517629	0.258814	−	0.965927i	$-0.416668\pi$
$683$	9.66545e54	0.517629	0.258814	+	0.965927i	$0.416668\pi$
$684$	7.83831e52	0.00407970
$685$	−3.26013e54	−0.164918
$686$	−3.81886e55	−1.87765
$687$	−1.32725e55	−0.634303
$688$	−3.56964e54	−0.165825
$689$	−3.25447e54	−0.146962
$690$	−1.33921e55	−0.587886
$691$	2.64597e55	1.12918	0.564589	−	0.825372i	$-0.309035\pi$
$691$	2.64597e55	1.12918	0.564589	+	0.825372i	$0.309035\pi$
$692$	−1.93160e55	−0.801396
$693$	−4.84205e54	−0.195313
$694$	−6.52823e54	−0.256027
$695$	4.92429e55	1.87776
$696$	1.19281e55	0.442274
$697$	−7.24105e53	−0.0261073
$698$	3.39755e55	1.19120
$699$	1.03449e55	0.352712
$700$	4.72297e55	1.56604
$701$	−1.37996e55	−0.445004	−0.222502	−	0.974932i	$-0.571422\pi$
$701$	−1.37996e55	−0.445004	−0.222502	+	0.974932i	$0.571422\pi$
$702$	6.42245e54	0.201431
$703$	−1.73463e54	−0.0529150
$704$	−4.42875e54	−0.131406
$705$	3.11705e55	0.899613
$706$	−1.31981e55	−0.370527
$707$	−1.23228e56	−3.36535
$708$	−5.12414e54	−0.136136
$709$	5.50079e55	1.42175	0.710876	−	0.703317i	$-0.248299\pi$
$709$	5.50079e55	1.42175	0.710876	+	0.703317i	$0.248299\pi$
$710$	2.71141e55	0.681801
$711$	7.03389e54	0.172083
$712$	−1.48500e55	−0.353482
$713$	3.38656e54	0.0784357
$714$	1.24660e54	0.0280940
$715$	−2.37335e55	−0.520467
$716$	6.34564e54	0.135416
$717$	−7.91440e55	−1.64359
$718$	−4.42777e55	−0.894868
$719$	5.53840e55	1.08936	0.544680	−	0.838644i	$-0.316651\pi$
$719$	5.53840e55	1.08936	0.544680	+	0.838644i	$0.316651\pi$
$720$	2.14790e54	0.0411178
$721$	−1.33430e54	−0.0248609
$722$	3.87325e55	0.702425
$723$	−4.36001e55	−0.769646
$724$	4.50969e55	0.774897
$725$	−1.20522e56	−2.01593
$726$	−4.78834e54	−0.0779689
$727$	5.80890e55	0.920817	0.460408	−	0.887707i	$-0.347703\pi$
$727$	5.80890e55	0.920817	0.460408	+	0.887707i	$0.347703\pi$
$728$	−1.28127e55	−0.197734
$729$	5.86109e55	0.880627
$730$	−1.14918e56	−1.68109
$731$	9.51990e53	0.0135595
$732$	−8.61215e53	−0.0119439
$733$	−1.18623e56	−1.60193	−0.800964	−	0.598713i	$-0.795679\pi$
$733$	−1.18623e56	−1.60193	−0.800964	+	0.598713i	$0.795679\pi$
$734$	7.73846e55	1.01761
$735$	3.26908e56	4.18622
$736$	−6.85002e54	−0.0854230
$737$	1.22058e56	1.48235
$738$	−7.65587e54	−0.0905514
$739$	−3.72382e55	−0.428966	−0.214483	−	0.976728i	$-0.568807\pi$
$739$	−3.72382e55	−0.428966	−0.214483	+	0.976728i	$0.568807\pi$
$740$	−4.75334e55	−0.533310
$741$	2.35756e54	0.0257637
$742$	5.99280e55	0.637902
$743$	−2.01398e55	−0.208820	−0.104410	−	0.994534i	$-0.533295\pi$
$743$	−2.01398e55	−0.208820	−0.104410	+	0.994534i	$0.533295\pi$
$744$	−5.95993e54	−0.0601962
$745$	−1.83649e56	−1.80693
$746$	−4.64480e54	−0.0445205
$747$	−1.14818e55	−0.107216
$748$	1.18111e54	0.0107450
$749$	1.59617e55	0.141477
$750$	−9.72605e55	−0.839928
$751$	3.30842e55	0.278382	0.139191	−	0.990266i	$-0.455550\pi$
$751$	3.30842e55	0.278382	0.139191	+	0.990266i	$0.455550\pi$
$752$	1.59436e55	0.130719
$753$	−2.41367e55	−0.192831
$754$	3.26959e55	0.254537
$755$	2.68378e55	0.203602
$756$	−1.18264e56	−0.874331
$757$	2.33076e56	1.67930	0.839648	−	0.543131i	$-0.182761\pi$
$757$	2.33076e56	1.67930	0.839648	+	0.543131i	$0.182761\pi$
$758$	−8.63140e55	−0.606082
$759$	−7.78608e55	−0.532849
$760$	−7.07466e54	−0.0471890
$761$	2.59131e55	0.168468	0.0842341	−	0.996446i	$-0.473156\pi$
$761$	2.59131e55	0.168468	0.0842341	+	0.996446i	$0.473156\pi$
$762$	7.28987e55	0.461953
$763$	−5.20675e56	−3.21616
$764$	1.23423e56	0.743150
$765$	−5.72824e53	−0.00336220
$766$	7.39272e55	0.423003
$767$	−1.40457e55	−0.0783490
$768$	1.20552e55	0.0655587
$769$	1.52577e56	0.808960	0.404480	−	0.914547i	$-0.367453\pi$
$769$	1.52577e56	0.808960	0.404480	+	0.914547i	$0.367453\pi$
$770$	4.37031e56	2.25914
$771$	−9.27470e55	−0.467455
$772$	−1.57961e56	−0.776267
$773$	3.31990e54	0.0159083	0.00795416	−	0.999968i	$-0.497468\pi$
$773$	3.31990e54	0.0159083	0.00795416	+	0.999968i	$0.497468\pi$
$774$	1.00653e55	0.0470302
$775$	6.02193e55	0.274380
$776$	−4.59450e55	−0.204143
$777$	−2.91680e56	−1.26385
$778$	−2.04404e56	−0.863750
$779$	2.52166e55	0.103922
$780$	6.46032e55	0.259662
$781$	1.57639e56	0.617972
$782$	1.82684e54	0.00698503
$783$	3.01788e56	1.12550
$784$	1.67212e56	0.608281
$785$	2.42547e56	0.860673
$786$	1.91648e55	0.0663383
$787$	5.51699e56	1.86292	0.931462	−	0.363839i	$-0.118534\pi$
$787$	5.51699e56	1.86292	0.931462	+	0.363839i	$0.118534\pi$
$788$	1.41249e56	0.465290
$789$	3.49896e56	1.12444
$790$	−6.34860e56	−1.99044
$791$	−7.79530e56	−2.38447
$792$	1.24877e55	0.0372684
$793$	−2.36066e54	−0.00687395
$794$	−2.02659e56	−0.575794
$795$	−3.02163e56	−0.837688
$796$	2.08896e56	0.565099
$797$	−4.73123e56	−1.24893	−0.624463	−	0.781055i	$-0.714682\pi$
$797$	−4.73123e56	−1.24893	−0.624463	+	0.781055i	$0.714682\pi$
$798$	−4.34124e55	−0.111830
$799$	−4.25200e54	−0.0106889
$800$	−1.21806e56	−0.298823
$801$	4.18724e55	0.100252
$802$	9.56070e54	0.0223403
$803$	−6.68123e56	−1.52371
$804$	−3.32244e56	−0.739545
$805$	6.75962e56	1.46860
$806$	−1.63367e55	−0.0346441
$807$	2.25257e56	0.466277
$808$	3.17806e56	0.642156
$809$	1.12022e56	0.220957	0.110478	−	0.993879i	$-0.464762\pi$
$809$	1.12022e56	0.220957	0.110478	+	0.993879i	$0.464762\pi$
$810$	6.56696e56	1.26446
$811$	−1.55868e55	−0.0292989	−0.0146495	−	0.999893i	$-0.504663\pi$
$811$	−1.55868e55	−0.0292989	−0.0146495	+	0.999893i	$0.504663\pi$
$812$	−6.02065e56	−1.10484
$813$	1.79886e56	0.322279
$814$	−2.76355e56	−0.483383
$815$	1.08959e57	1.86076
$816$	−3.21501e54	−0.00536073
$817$	−3.31526e55	−0.0539743
$818$	3.33020e54	0.00529396
$819$	3.61279e55	0.0560799
$820$	6.90998e56	1.04739
$821$	−3.16630e56	−0.468663	−0.234331	−	0.972157i	$-0.575290\pi$
$821$	−3.16630e56	−0.468663	−0.234331	+	0.972157i	$0.575290\pi$
$822$	5.15936e55	0.0745754
$823$	3.30351e56	0.466315	0.233157	−	0.972439i	$-0.425094\pi$
$823$	3.30351e56	0.466315	0.233157	+	0.972439i	$0.425094\pi$
$824$	3.44119e54	0.00474381
$825$	−1.38451e57	−1.86399
$826$	2.58639e56	0.340081
$827$	2.57779e56	0.331047	0.165523	−	0.986206i	$-0.447069\pi$
$827$	2.57779e56	0.331047	0.165523	+	0.986206i	$0.447069\pi$
$828$	1.93149e55	0.0242271
$829$	−2.58133e56	−0.316250	−0.158125	−	0.987419i	$-0.550545\pi$
$829$	−2.58133e56	−0.316250	−0.158125	+	0.987419i	$0.550545\pi$
$830$	1.03632e57	1.24014
$831$	−6.07596e56	−0.710223
$832$	3.30442e55	0.0377303
$833$	−4.45939e55	−0.0497391
$834$	−7.79301e56	−0.849116
$835$	−1.17100e57	−1.24644
$836$	−4.11315e55	−0.0427713
$837$	−1.50790e56	−0.153188
$838$	5.59975e56	0.555789
$839$	1.04524e57	1.01358	0.506792	−	0.862068i	$-0.330831\pi$
$839$	1.04524e57	1.01358	0.506792	+	0.862068i	$0.330831\pi$
$840$	−1.18961e57	−1.12709
$841$	4.56118e56	0.422236
$842$	−3.60762e56	−0.326313
$843$	1.91759e56	0.169479
$844$	5.57798e56	0.481725
$845$	−1.76655e57	−1.49080
$846$	−4.49558e55	−0.0370735
$847$	2.41689e56	0.194774
$848$	−1.54555e56	−0.121721
$849$	7.42892e56	0.571776
$850$	3.24845e55	0.0244347
$851$	−4.27443e56	−0.314233
$852$	−4.29098e56	−0.308308
$853$	4.21887e56	0.296272	0.148136	−	0.988967i	$-0.452673\pi$
$853$	4.21887e56	0.296272	0.148136	+	0.988967i	$0.452673\pi$
$854$	4.34694e55	0.0298370
$855$	1.99483e55	0.0133834
$856$	−4.11655e55	−0.0269957
$857$	1.69567e57	1.08696	0.543481	−	0.839422i	$-0.317106\pi$
$857$	1.69567e57	1.08696	0.543481	+	0.839422i	$0.317106\pi$
$858$	3.75597e56	0.235353
$859$	1.88412e57	1.15409	0.577047	−	0.816711i	$-0.304205\pi$
$859$	1.88412e57	1.15409	0.577047	+	0.816711i	$0.304205\pi$
$860$	−9.08465e56	−0.543987
$861$	4.24019e57	2.48213
$862$	−1.81597e57	−1.03924
$863$	3.08841e57	1.72792	0.863960	−	0.503560i	$-0.167977\pi$
$863$	3.08841e57	1.72792	0.863960	+	0.503560i	$0.167977\pi$
$864$	3.05003e56	0.166835
$865$	−4.91586e57	−2.62897
$866$	−1.46794e57	−0.767557
$867$	−2.05088e57	−1.04850
$868$	3.00825e56	0.150376
$869$	−3.69103e57	−1.80410
$870$	3.03567e57	1.45087
$871$	−9.10708e56	−0.425623
$872$	1.34283e57	0.613689
$873$	1.29550e56	0.0578977
$874$	−6.36187e55	−0.0278043
$875$	4.90918e57	2.09822
$876$	1.81865e57	0.760184
$877$	−7.61249e56	−0.311196	−0.155598	−	0.987820i	$-0.549730\pi$
$877$	−7.61249e56	−0.311196	−0.155598	+	0.987820i	$0.549730\pi$
$878$	−2.94240e56	−0.117641
$879$	−3.86385e57	−1.51090
$880$	−1.12711e57	−0.431075
$881$	2.56093e57	0.958003	0.479001	−	0.877814i	$-0.340999\pi$
$881$	2.56093e57	0.958003	0.479001	+	0.877814i	$0.340999\pi$
$882$	−4.71485e56	−0.172517
$883$	−1.90238e57	−0.680871	−0.340435	−	0.940268i	$-0.610574\pi$
$883$	−1.90238e57	−0.680871	−0.340435	+	0.940268i	$0.610574\pi$
$884$	−8.81259e54	−0.00308521
$885$	−1.30408e57	−0.446592
$886$	−2.00925e57	−0.673096
$887$	−3.06239e57	−1.00357	−0.501787	−	0.864991i	$-0.667324\pi$
$887$	−3.06239e57	−1.00357	−0.501787	+	0.864991i	$0.667324\pi$
$888$	7.52246e56	0.241161
$889$	−3.67953e57	−1.15400
$890$	−3.77930e57	−1.15959
$891$	3.81798e57	1.14609
$892$	1.41074e57	0.414317
$893$	1.48074e56	0.0425476
$894$	2.90637e57	0.817089
$895$	1.61495e57	0.444231
$896$	−6.08480e56	−0.163772
$897$	5.80942e56	0.152996
$898$	4.49949e57	1.15951
$899$	−7.67651e56	−0.193575
$900$	3.43454e56	0.0847501
$901$	4.12184e55	0.00995309
$902$	4.01741e57	0.949333
$903$	−5.57463e57	−1.28915
$904$	2.01042e57	0.454990
$905$	1.14770e58	2.54204
$906$	−4.24726e56	−0.0920680
$907$	7.47448e57	1.58577	0.792883	−	0.609374i	$-0.208579\pi$
$907$	7.47448e57	1.58577	0.792883	+	0.609374i	$0.208579\pi$
$908$	−3.50707e57	−0.728233
$909$	−8.96112e56	−0.182124
$910$	−3.26081e57	−0.648662
$911$	−7.47540e57	−1.45555	−0.727773	−	0.685818i	$-0.759445\pi$
$911$	−7.47540e57	−1.45555	−0.727773	+	0.685818i	$0.759445\pi$
$912$	1.11961e56	0.0213387
$913$	6.02509e57	1.12404
$914$	−6.41337e57	−1.17121
$915$	−2.19177e56	−0.0391817
$916$	−1.72774e57	−0.302354
$917$	−9.67333e56	−0.165720
$918$	−8.13415e55	−0.0136421
$919$	−1.13700e58	−1.86685	−0.933424	−	0.358774i	$-0.883195\pi$
$919$	−1.13700e58	−1.86685	−0.933424	+	0.358774i	$0.883195\pi$
$920$	−1.74331e57	−0.280229
$921$	1.02914e58	1.61962
$922$	1.22400e57	0.188595
$923$	−1.17619e57	−0.177437
$924$	−6.91629e57	−1.02157
$925$	−7.60071e57	−1.09923
$926$	9.90176e56	0.140216
$927$	−9.70306e54	−0.00134541
$928$	1.55273e57	0.210820
$929$	1.03649e57	0.137804	0.0689018	−	0.997623i	$-0.478050\pi$
$929$	1.03649e57	0.137804	0.0689018	+	0.997623i	$0.478050\pi$
$930$	−1.51679e57	−0.197473
$931$	1.55296e57	0.197989
$932$	1.34663e57	0.168128
$933$	3.65972e57	0.447462
$934$	−3.31605e56	−0.0397061
$935$	3.00589e56	0.0352490
$936$	−9.31743e55	−0.0107008
$937$	−3.19654e57	−0.359549	−0.179774	−	0.983708i	$-0.557537\pi$
$937$	−3.19654e57	−0.359549	−0.179774	+	0.983708i	$0.557537\pi$
$938$	1.67699e58	1.84746
$939$	−4.10770e57	−0.443220
$940$	4.05760e57	0.428821
$941$	1.79945e58	1.86269	0.931347	−	0.364134i	$-0.118635\pi$
$941$	1.79945e58	1.86269	0.931347	+	0.364134i	$0.118635\pi$
$942$	−3.83847e57	−0.389193
$943$	6.21379e57	0.617132
$944$	−6.67032e56	−0.0648922
$945$	−3.00978e58	−2.86823
$946$	−5.28174e57	−0.493060
$947$	−4.51918e57	−0.413271	−0.206635	−	0.978418i	$-0.566251\pi$
$947$	−4.51918e57	−0.413271	−0.206635	+	0.978418i	$0.566251\pi$
$948$	1.00471e58	0.900071
$949$	4.98506e57	0.437501
$950$	−1.13126e57	−0.0972637
$951$	4.24473e57	0.357545
$952$	1.62276e56	0.0133916
$953$	−1.76691e58	−1.42857	−0.714285	−	0.699855i	$-0.753248\pi$
$953$	−1.76691e58	−1.42857	−0.714285	+	0.699855i	$0.753248\pi$
$954$	4.35797e56	0.0345216
$955$	3.14109e58	2.43789
$956$	−1.03025e58	−0.783456
$957$	1.76491e58	1.31505
$958$	1.75941e58	1.28452
$959$	−2.60416e57	−0.186297
$960$	3.06801e57	0.215064
$961$	−1.41746e58	−0.973653
$962$	2.06197e57	0.138793
$963$	1.16074e56	0.00765634
$964$	−5.67562e57	−0.366869
$965$	−4.02006e58	−2.54653
$966$	−1.06975e58	−0.664094
$967$	−1.51301e58	−0.920503	−0.460252	−	0.887788i	$-0.652241\pi$
$967$	−1.51301e58	−0.920503	−0.460252	+	0.887788i	$0.652241\pi$
$968$	−6.23319e56	−0.0371656
$969$	−2.98590e55	−0.00174486
$970$	−1.16929e58	−0.669689
$971$	6.54738e57	0.367530	0.183765	−	0.982970i	$-0.441172\pi$
$971$	6.54738e57	0.367530	0.183765	+	0.982970i	$0.441172\pi$
$972$	−1.81587e57	−0.0999063
$973$	3.93348e58	2.12118
$974$	−6.35976e57	−0.336156
$975$	1.03302e58	0.535204
$976$	−1.12108e56	−0.00569332
$977$	5.96738e57	0.297057	0.148529	−	0.988908i	$-0.452546\pi$
$977$	5.96738e57	0.297057	0.148529	+	0.988908i	$0.452546\pi$
$978$	−1.72435e58	−0.841429
$979$	−2.19725e58	−1.05104
$980$	4.25550e58	1.99546
$981$	−3.78635e57	−0.174050
$982$	−1.53289e58	−0.690774
$983$	−2.51216e58	−1.10982	−0.554912	−	0.831909i	$-0.687248\pi$
$983$	−2.51216e58	−1.10982	−0.554912	+	0.831909i	$0.687248\pi$
$984$	−1.09355e58	−0.473624
$985$	3.59474e58	1.52638
$986$	−4.14099e56	−0.0172387
$987$	2.48987e58	1.01623
$988$	3.06894e56	0.0122808
$989$	−8.16935e57	−0.320523
$990$	3.17809e57	0.122259
$991$	5.48377e57	0.206844	0.103422	−	0.994638i	$-0.467021\pi$
$991$	5.48377e57	0.206844	0.103422	+	0.994638i	$0.467021\pi$
$992$	−7.75830e56	−0.0286939
$993$	−1.89238e58	−0.686275
$994$	2.16585e58	0.770183
$995$	5.31634e58	1.85380
$996$	−1.64005e58	−0.560788
$997$	3.05936e58	1.02583	0.512915	−	0.858439i	$-0.328566\pi$
$997$	3.05936e58	1.02583	0.512915	+	0.858439i	$0.328566\pi$
$998$	−1.97933e58	−0.650837
$999$	1.90322e58	0.613710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.40.a.b.1.2	✓	2
3.2	odd	2		18.40.a.e.1.1		2
4.3	odd	2		16.40.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.40.a.b.1.2	✓	2	1.1	even	1	trivial
16.40.a.b.1.1		2	4.3	odd	2
18.40.a.e.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-524288. q^{2} +2.11161e9 q^{3} +2.74878e11 q^{4} +6.99557e13 q^{5} -1.10709e15 q^{6} +5.58800e16 q^{7} -1.44115e17 q^{8} +4.06359e17 q^{9} +O(q^{10})\)	\(q-524288. q^{2} +2.11161e9 q^{3} +2.74878e11 q^{4} +6.99557e13 q^{5} -1.10709e15 q^{6} +5.58800e16 q^{7} -1.44115e17 q^{8} +4.06359e17 q^{9} -3.66769e19 q^{10} -2.13237e20 q^{11} +5.80436e20 q^{12} +1.59102e21 q^{13} -2.92972e22 q^{14} +1.47719e23 q^{15} +7.55579e22 q^{16} -2.01506e22 q^{17} -2.13049e23 q^{18} +7.01734e23 q^{19} +1.92293e25 q^{20} +1.17997e26 q^{21} +1.11797e26 q^{22} +1.72919e26 q^{23} -3.04316e26 q^{24} +3.07481e27 q^{25} -8.34153e26 q^{26} -7.69936e27 q^{27} +1.53602e28 q^{28} -3.91965e28 q^{29} -7.74476e28 q^{30} +1.95847e28 q^{31} -3.96141e28 q^{32} -4.50274e29 q^{33} +1.05647e28 q^{34} +3.90913e30 q^{35} +1.11699e29 q^{36} -2.47193e30 q^{37} -3.67911e29 q^{38} +3.35962e30 q^{39} -1.00817e31 q^{40} +3.59347e31 q^{41} -6.18644e31 q^{42} -4.72438e31 q^{43} -5.86141e31 q^{44} +2.84272e31 q^{45} -9.06593e31 q^{46} +2.11011e32 q^{47} +1.59549e32 q^{48} +2.21303e33 q^{49} -1.61209e33 q^{50} -4.25503e31 q^{51} +4.37337e32 q^{52} -2.04552e33 q^{53} +4.03668e33 q^{54} -1.49171e34 q^{55} -8.05316e33 q^{56} +1.48179e33 q^{57} +2.05502e34 q^{58} -8.82809e33 q^{59} +4.06048e34 q^{60} -1.48374e33 q^{61} -1.02680e34 q^{62} +2.27074e34 q^{63} +2.07692e34 q^{64} +1.11301e35 q^{65} +2.36073e35 q^{66} -5.72405e35 q^{67} -5.53895e33 q^{68} +3.65138e35 q^{69} -2.04951e36 q^{70} -7.39268e35 q^{71} -5.85626e34 q^{72} +3.13325e36 q^{73} +1.29600e36 q^{74} +6.49282e36 q^{75} +1.92891e35 q^{76} -1.19157e37 q^{77} -1.76141e36 q^{78} +1.73095e37 q^{79} +5.28570e36 q^{80} -1.79049e37 q^{81} -1.88401e37 q^{82} -2.82554e37 q^{83} +3.24348e37 q^{84} -1.40965e36 q^{85} +2.47694e37 q^{86} -8.27678e37 q^{87} +3.07307e37 q^{88} +1.03043e38 q^{89} -1.49040e37 q^{90} +8.89063e37 q^{91} +4.75316e37 q^{92} +4.13553e37 q^{93} -1.10631e38 q^{94} +4.90903e37 q^{95} -8.36497e37 q^{96} +3.18808e38 q^{97} -1.16027e39 q^{98} -8.66508e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots - 31\!\cdots\!86 q^{9}+O(q^{10}) \) 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9	\( 2 q - 1048576 q^{2} + 287418264 q^{3} + 549755813888 q^{4} + 53622738166620 q^{5} - 150689946796032 q^{6} + 74\!\cdots\!12 q^{7}+ \cdots + 72\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 1048576 * q^2 + 287418264 * q^3 + 549755813888 * q^4 + 53622738166620 * q^5 - 150689946796032 * q^6 + 7497991625846512 * q^7 - 288230376151711744 * q^8 - 318504822486858486 * q^9 - 28113758147900866560 * q^10 - 432928873549526253816 * q^11 + 79004930825798025216 * q^12 - 1110716884377980399156 * q^13 - 3931107033531816083456 * q^14 + 177514053087296176226640 * q^15 + 151115727451828646838272 * q^16 - 361727800957394760654108 * q^17 + 166988256371990061907968 * q^18 + 11531090014904148017962360 * q^19 + 14739706031846649527009280 * q^20 + 206255336094912268749797184 * q^21 + 226979413255534020560683008 * q^22 + 733399930716618125168143824 * q^23 - 41421337172795995044446208 * q^24 + 1522590281438531446348943150 * q^25 + 582335533876762587512700928 * q^26 + 1015590507281331347888066160 * q^27 + 2061032244396328790762979328 * q^28 - 66283478621079021435470040660 * q^29 - 93068487865032337641512632320 * q^30 - 186790705491150225840859566656 * q^31 - 79228162514264337593543950336 * q^32 - 49512382311136707894463876512 * q^33 + 189649545308350584273820975104 * q^34 + 4699349644576524589906668345120 * q^35 - 87549938956757925577604726784 * q^36 + 2975477658591913559588340321052 * q^37 - 6045612121734065956041449799680 * q^38 + 8288123926734148196202973745808 * q^39 - 7727850996024816187216641392640 * q^40 + 16770326730060018362152407596724 * q^41 - 108137197650529363558293666004992 * q^42 - 9812395004866851368387130850616 * q^43 - 119002582616917420571719372898304 * q^44 + 40266363304618629851608344270540 * q^45 - 384512782875554283608155789197312 * q^46 + 672278426349701905666521369769632 * q^47 + 21716710023650866649862613499904 * q^48 + 3644309465778284633118680596157586 * q^49 - 798275813474844774943394706227200 * q^50 + 580553528426174218705101873396144 * q^51 - 305311532385180103481858944139264 * q^52 - 8761864571633558324701150169407236 * q^53 - 532461915881514649721538430894080 * q^54 - 11328905370645770966149273576022160 * q^55 - 1080574473350062429051540905918464 * q^56 - 18273076268563776391813920538819680 * q^57 + 34751632439288277990359716677550080 * q^58 - 12819225750671101391169533921560920 * q^59 + 48794691365782074237393374973788160 * q^60 - 20956924322550570450554426592045716 * q^61 + 97932125400544169605652580482940928 * q^62 + 57777775631084010576555882975543984 * q^63 + 41538374868278621028243970633760768 * q^64 + 155428501009224030268997780328195240 * q^65 + 25958747897141242308572676888723456 * q^66 - 430210910797386482647696776154188008 * q^67 - 99430980810624511127753051395325952 * q^68 - 657289380718196443693542397362196032 * q^69 - 2463812626455736924192987333326274560 * q^70 - 505835127408773713626404787885403536 * q^71 + 45901382395760699285231226996129792 * q^72 + 5225008613368893844954971696153387124 * q^73 - 1560007230667837176329451770243710976 * q^74 + 9324378759630332095186368293653381800 * q^75 + 3169641888079709971961059632574627840 * q^76 - 1286526284405007303669629309781343296 * q^77 - 4345363917299593089490864699242184704 * q^78 + 5133106059230199144047658337509305440 * q^79 + 4051619543003858829163438482464440320 * q^80 - 30865091955632000468542250095184041518 * q^81 - 8792481060649706907056161474071232512 * q^82 - 64869811713330760861780892502955295496 * q^83 + 56695035081800738961250669562425245696 * q^84 + 4169326167850982553612360321923472120 * q^85 + 5144520952311631770228952059407761408 * q^86 - 33355767685492704090236226944356001520 * q^87 + 62391626035058400596705606578106007552 * q^88 - 35854914207967073080588387127246110380 * q^89 - 21111171084251892207640035600912875520 * q^90 + 219621888597383210927045163285292559264 * q^91 + 201595437908258604244352782406680313856 * q^92 + 417824530946031783400120882011006743808 * q^93 - 352467511594032512718089155913780822016 * q^94 - 127785377061536603773906538331287257200 * q^95 - 11385810464879865574123169906637668352 * q^96 - 145570707650873901517300801294356641468 * q^97 - 1910667721193965293728526812398268448768 * q^98 + 72596170648714013699688849065341538088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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